I don't know where you live but it's quite unusual here to be cycling through areas that have a lot of pedestrians. If the bike lane is a dedicated one, pedestrians are very rarely in it. But yes if all else fails, the road is preferable to the pavement if you're unwilling to cycle slowly enough.
> how do you prevent pedestrians from crossing said dedicated infrastructure without looking?
That's a UX problem. You can also ask how to prevent cars driving on the cycle lane. Which we do in a multitude of ways. You just need to physically communicate segregation and danger.
> A court will rule in favor of the pedestrian stepping onto a bike lane without looking getting hit by a bike that's too close to do anything?
Here, absolutely, if they consider the cyclist is going too fast for the conditions. There's a concept of a hierarchy whereby the more vulnerable class is almost assumed not to be at fault. Same for a car hitting a cyclist, or a motorbike, even.